The daily number of cheques presented at a local branch of a certain bank to be cashed has the following probability mass function (a Poisson distribution with parameter ):

for

If each cheque presented has a probability to be refused (due to the lack of sufficient funds), compute the pmf, for , of the daily number of refused cheques.
A hint was provided as follows: You may first compute the conditional probability and then use the total probability formula by summing over all possible values of .

I'm still grasping the concepts behind Poisson distributions, so any help would be appreciated.